be_map1512 Over 100 posts !
Posts : 141 Join date : 20101114
 Subject: Material conditional Sun Nov 21, 2010 9:10 am  
 The material conditional, also known as material implication, is a binary truth function → such that the compound sentence p→q (typically read "if p then q") is logically equivalent to the negative compound: not(p and not q). A material conditional compound itself is often simply called a conditional. By definition of "→", the compound p→q is false if and only if both p is true and q is false. That is to say that p→q is true if and only if either p is false or q is true (or both). Thus → is a function from pairs of truth values of the components p, q to truth values of the compound p→q, whose truth value is entirely a function of the truth values of the components. Thus p→q is said to be truthfunctional. p→q is logically equivalent also to ¬p∨q (either not p, or q (or both)), and to ¬q → ¬p (if not q then not p), but not to ¬p → ¬q. For convenience, p→q is typically read "If p, then q", "p only if q", or "q if p". Saying "It is false that if p then q" does not always sound logically equivalent in everyday English to saying "both p and not q" but, when used in logic, it is taken as logically equivalent. (Other senses of English "if...then..." require other logical forms.) silver charm braceletshouses for sale 

gaunpro Over 100 posts !
Posts : 301 Join date : 20101126
 Subject: Re: Material conditional Tue Dec 21, 2010 5:19 am  
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